Dominic opened a savings account with a $500 deposit. His account pays 2% simple interest annually. Evie also opened a savings account with a $500 deposit. Her account pays 2% interest compounded annually. How much more interest will Evie's $500 deposit have earned after 3 years than Dominic's $500 deposit in the same amount of time?

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

what